$a-0.19,b-0.05, c-0.17,d-0.08,e-0.40,f-0.11$
Since it is relative frequency we can multiply each with $100$ and result remains the same.
$a-19,b-5, c-17,d-8,e-40,f-11$
For Assigning prefix binary code lets first create the Huffman tree
$(1) \ a-19,{\color{Red} {b-5} },c-17,{\color{Red} {d-8} },e-40,f-11$
$(2) \ a-19,{\color{Red} {(b,d)-13} },c-17,e-40,{\color{Red} {f-11} }$
$(3) \ {\color{Red} {a-19} },(b,d,f)-24,{\color{Red} {c-17} },e-40$
$(4) \ {\color{Red} {(a,c)-36,(b,d,f)-24}},e-40$
$(5) \ {\color{Red} {(a,b,c,d,f)-60,e-40}}$
Now put $0$ on each of the left edges and $1$ on each of the right edges as shown below
$\text{Prefix code}$ = Traverse from the root node to the leaf node and write the symbol $(1 \ or \ 0)$ present on each edge.
- For $a$ the prefix code is $111$ i.e. $3$ bits
- For $b$ the prefix code is $1010$ i.e. $4$ bits
- For $c$ the prefix code is $110$ i.e. $3$ bits
- For $d$ the prefix code is $1011$ i.e. $4$ bits
- For $e$ the prefix code is $0$ i.e. $1$ bits
- For $f$ the prefix code is $100$ i.e. $3$ bits
And the average length of encoded words $=\dfrac{(19\times 3)+(5\times 4)+(17\times 3)+(8\times 4)+(40\times 1)+(11\times 3)}{100}$
$\quad =\dfrac{57+20+51+32+40+33}{100}$
$\quad =\dfrac{233}{100}$
$\quad =2.33$